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Single- and two-stage cross-sectional and time series benchmarking procedures for small area estimation

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  • Danny Pfeffermann
  • Anna Sikov
  • Richard Tiller

Abstract

This article is divided into two parts. In the first part, we review and study the properties of single-stage cross-sectional and time series benchmarking procedures that have been proposed in the literature in the context of small area estimation. We compare cross-sectional and time series benchmarking empirically, using data generated from a time series model which complies with the familiar Fay–Herriot model at any given time point. In the second part, we review cross-sectional methods proposed for benchmarking hierarchical small areas and develop a new two-stage benchmarking procedure for hierarchical time series models. The latter procedure is applied to monthly unemployment estimates in Census Divisions and States of the USA. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • Danny Pfeffermann & Anna Sikov & Richard Tiller, 2014. "Single- and two-stage cross-sectional and time series benchmarking procedures for small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 631-666, December.
    • Handle: RePEc:spr:testjl:v:23:y:2014:i:4:p:631-666
    DOI: 10.1007/s11749-014-0398-y
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    References listed on IDEAS

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    1. J. Durbin & B. Quenneville, 1997. "Benchmarking by State Space Models," International Statistical Review, International Statistical Institute, vol. 65(1), pages 23-48, April.
    2. G. Datta & M. Ghosh & R. Steorts & J. Maples, 2011. "Bayesian benchmarking with applications to small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 574-588, November.
    3. Tommaso Di Fonzo & Marco Marini, 2011. "Simultaneous and two‐step reconciliation of systems of time series: methodological and practical issues," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 60(2), pages 143-164, March.
    4. Pfeffermann, Danny & Barnard, Charles H, 1991. "Some New Estimators for Small-Area Means with Application to the Assessment of Farmland Values," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(1), pages 73-84, January.
    5. Doran, Howard E, 1992. "Constraining Kalman Filter and Smoothing Estimates to Satisfy Time-Varying Restrictions," The Review of Economics and Statistics, MIT Press, vol. 74(3), pages 568-572, August.
    6. Peter Hall & Tapabrata Maiti, 2006. "On parametric bootstrap methods for small area prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 221-238, April.
    7. Pfeffermann, Danny & Tiller, Richard, 2006. "Small-Area Estimation With StateSpace Models Subject to Benchmark Constraints," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1387-1397, December.
    8. M. Ugarte & A. Militino & T. Goicoa, 2009. "Benchmarked estimates in small areas using linear mixed models with restrictions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 342-364, August.
    9. Malay Ghosh & Rebecca Steorts, 2013. "Two-stage benchmarking as applied to small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(4), pages 670-687, November.
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    Cited by:

    1. Domingo Morales, 2019. "Comments on: Deville and Särndal’s calibration: revisiting a 25 years old successful optimization problem," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1068-1070, December.
    2. Oksana Bollineni‐Balabay & Jan van den Brakel & Franz Palm & Harm Jan Boonstra, 2017. "Multilevel hierarchical Bayesian versus state space approach in time series small area estimation: the Dutch Travel Survey," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1281-1308, October.
    3. Elaheh Torkashvand & Mohammad Jafari Jozani & Mahmoud Torabi, 2016. "Constrained Bayes estimation in small area models with functional measurement error," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(4), pages 710-730, December.
    4. Newhouse,David Locke & Merfeld,Joshua David & Ramakrishnan,Anusha Pudugramam & Swartz,Tom & Lahiri,Partha, 2022. "Small Area Estimation of Monetary Poverty in Mexico Using Satellite Imagery and Machine Learning," Policy Research Working Paper Series 10175, The World Bank.
    5. Masaki,Takaaki & Newhouse,David Locke & Silwal,Ani Rudra & Bedada,Adane & Engstrom,Ryan, 2020. "Small Area Estimation of Non-Monetary Poverty with Geospatial Data," Policy Research Working Paper Series 9383, The World Bank.
    6. Nikos Tzavidis & Li‐Chun Zhang & Angela Luna & Timo Schmid & Natalia Rojas‐Perilla, 2018. "From start to finish: a framework for the production of small area official statistics," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 927-979, October.
    7. Zhang Junni L. & Bryant John, 2020. "Fully Bayesian Benchmarking of Small Area Estimation Models," Journal of Official Statistics, Sciendo, vol. 36(1), pages 197-223, March.
    8. Benavent, Roberto & Morales, Domingo, 2016. "Multivariate Fay–Herriot models for small area estimation," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 372-390.
    9. Paul A. Smith & Chiara Bocci & Nikos Tzavidis & Sabine Krieg & Marc J. E. Smeets, 2021. "Robust estimation for small domains in business surveys," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(2), pages 312-334, March.
    10. Rebecca Steorts & M. Ugarte, 2014. "Comments on: “Single and two-stage cross-sectional and time series benchmarking procedures for small area estimation”," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 680-685, December.

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